I am having issues solving this Differential Equation using dsolve
DEQ:
dT/dt = (A1*exp(1i*(w*t+phi))+A1)*(B1*exp(1i*w*t)-T(t))
CODE:
A1 = 7.9443e-5;B1 = 10; w = 7.3e-5;phi = 0;syms T(t)ode = diff(T) == (A1*exp(1i*(w*t+phi))+A1)*(B1*exp(1i*w*t)-T);cond = T(0) == 10;TSol(t) = dsolve(ode,cond);
%The solution comes out to be:
TSol = exp(-(5861854777884531*dt)/73786976294838206464 + ... (exp((dt*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063) * ... int((29309273889422655*exp(x*(5861854777884531/73786976294838206464 + ... 16159347808569567i/147573952589676412928) - ... (exp((x*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063) * ... cos((5386449269523189*x)/147573952589676412928))/18446744073709551616, ... x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + ... 10*exp(- (5861854777884531*t)/73786976294838206464 + ... (exp((t*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063) * ... exp(-1953951592628177i/1795483089841063)
I dont understand what this portion of the solution or the rest of it means.
int((29309273889422655*exp(x*(5861854777884531/73786976294838206464 + 16159347808569567i/147573952589676412928) – (exp((x*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063)*cos((5386449269523189*x)/147573952589676412928))/18446744073709551616, x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)
Is it possible for someone to explain why I get (x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) in my solution and how do I fix it to get a proper analytical solution. I am running MATLAB R2019a.
I solved a similar differential equation seen below and this work using dsolve so I am not sure why my current DEQ doesn't work:
DEQ: dT/dt = (A1*exp(1i*(w*t+phi)))*(B1*exp(1i*w*t)-T(t))
Best Answer